The Ferraris of Sebastian Vettel and Kimi Raikkonen collided on the first lap and Rosberg's Mercedes teammate Lewis Hamilton lost his front wing after getting caught up in the incident.
Vettel recovered to finish second with Daniil Kvyat completing the podium for Red Bull, but there was a pointed exchange between the pair at the end of the race in Shanghai.
Four-time champion Vettel blamed Russia's Kvyat for the crash which saw the Ferraris come together.
"You came like a torpedo," he said. "I was racing," responded Kyvat with a sheepish grin.
"You were lucky this time," retorted Vettel before both headed off to the podium presentations.
Hamilton, who started from the back of the grid, made five pit stops during the course of the 56 laps, but battled to finish seventh in a car compromised by the earlier damage.
Rosberg was winning his sixth race in a row having dominated the back end of last season after Hamilton wrapped up his third world title.
With maximum points from three races, he leads this year's 21-round championship by 36 points from Hamilton.
Rosberg was briefly headed by Red Bull's Daniel Ricciardo from the start, but the Australian was another driver to suffer cruel luck, as his left rear tire punctured with debris flying on to the track.
After the safety car was deployed, Ricciardo and others were able to recover lost time and he eventually finished a fine fourth, overtaking Hamilton on the way in his charge through the field.
Raikkonen took a battling fifth and Felipe Massa was sixth in the Williams.
Ricciardo is third in the title race, three points behind Hamilton, with Vettel fourth, a further three points back, but they all face a real fight to catch Rosberg, who is in the form of his life.
"The start was not quite good enough with Daniel but then I had a really quick car today, really great, attacked straight away and was able to pull a big gap after that," he said at the presentations.